Amid Egypt's ongoing civil unrest, at least 25 women have been sexually assaulted during clashes in Tahrir Square, according to local women's rights campaigners.

In a typical attack, crowds of men quickly surround isolated women, groping them and attempting to remove their clothes. Some women have been stripped naked and one was raped, the campaigners said.

Since Thursday, hundreds of thousands of Egyptians have taken to the streets in 12 of the country's 21 provinces to protest against President Mohamed Morsi, the Muslim Brotherhood, and police brutality – two years after the start of the revolution that toppled Hosni Mubarak.

Last night Morsi declared a 30-day state of emergency and curfew in the three Suez canal provinces – Port Said, Ismailiya and Suez – hit hardest by the latest wave of political violence.

The president vowed in a televised address on Sunday last night that he would not hesitate to take more action to stem the latest eruption of violence across much of the country. But at the same time, he sought to reassure Egyptians that his latest moves would not plunge the country back into authoritarianism.

"There is no going back on freedom, democracy and the supremacy of the law," he said.

Opposition spokesman Khaled Dawoud blamed Morsi's policies for the unrest, and said he wanted more details about the president's invitation to senior politicians to meet for a dialogue later today.

More than 40 people have died and more than 500 have been injured in clashes in cities including Alexandra, Suez and Mahalla in the past four days. On Saturday, the government lost control of Port Said, a city on the Mediterranean, when hardcore football fans rioted over being scapegoated, as they saw it, by security forces for the mass deaths at a football match in February last year. Thirty-two people died in the riots, with the situation inflamed again on Sunday when police disrupted a funeral march for those killed the day before, state media reported.

Elsewhere, the Islamist leader Tareq el-Zomr hinted that his followers may start to form their own militias to "counter the aggression on innocent citizens".

For four days in Cairo, police armed with teargas have clashed with stone-throwing protesters in and around the crowded Tahrir Square, where the sexual assaults are reported to have taken place.

"This Friday was one of the worst that we have witnessed [for sexual assaults]," said Leil-Zahra Mortada, a spokesman for Operation Anti-Sexual Harassment (OpAntiSH) , a group set up in November to rescue assault victims from Tahrir Square.

"All of the cases were really, really bad," Mortada told the Guardian. "But the worst case that we dealt with involved a bladed weapon being used on the private parts of an assaulted woman." OpAntiSH treated 16 women, while Tahrir Bodyguard, another rescue group, helped nine, making a total of 25 – with the two teams hearing reports of at least nine more.

It is not certain who is behind the attacks, but OpAntiSH believes they are organised by those opposed to the protests. "We believe they must be organised, because they happen most of the time in the exact same spots in Tahrir Square and they use the same methodologies," Mortada said, adding that the testimonies OpAntiSH had collected were similar to accounts of attacks in 2005 thought to have been instigated by secret police.

In December, an Unreported World documentary for Channel 4 interviewed men who claimed to have been paid to assault women in Tahrir.

"It happens very quickly," said one victim, a protester who was assaulted on a street leading to the square, and who spoke to the Guardian on condition of anonymity. "Suddenly there were six men on one side of me, and six on the other, and they just started scratching me all the way down my skin. It's not just sexual assault. It's like they actually want to hurt you."

On days when large clashes are expected in Tahrir, witnesses to assaults can now call a hotline staffed by OpAntiSH, which then sends mixed-gender teams to try to rescue the women. Carrying flares to frighten away the assailants and clothes to cover the victims, the teams take them to one of a dozen safe houses in the surrounding area, where they are given medical, psychological and legal support.

"It makes you so angry," said the assaulted protester, who spoke to the Guardian on condition of anonymity. "You are reminded just how vulnerable you are as a woman. There is nothing you can do except not go to the square, or be protected by men – and even that doesn't always work."

Nevertheless, empowered by the experience, two women rescued on Friday have since joined OpAntiSH themselves.

"We cannot accept it anymore," said a representative from Tahrir Bodyguard,, who says the attacks were part of a wider culture of sexual harassment prevalent throughout Egypt. "We need to tackle this problem, not only in Tahrir Square, not only in Cairo, but in Egypt as a whole."